If the probability of getting at least one pair of matching dice when rolling five 6-sided dice is , where and are positive co-prime integers, then what is ?
Note: Three-of-a-kind, four-of-a-kind, full house, yahtzee, or two pairs would all count as "at least one pair of matching dice." However, a straight ( or ) or a small straight would not count.
Check out The anti-Yahtzee first to make finding the solution to this problem trivial.